3. DIFFERENT REPRESENTATIONS
OF THE REAL NUMBERS x Î [0,1]

There are the following main ways for representing and interpreting real numbers xÎ D.

1. As an individual geometrical point x of the segment [0,1].

2. In an arbitrary, for example, binary positional number system:

as an infinite sequence of binary digits:

x = 0 . a1 a2 a3 ... an..., where " n ((an=0) Ú (an=1)).

3. As the infinite sum:  

x = åi = 1¥  ai2-i

( x£ 1).

4. As an ¥ -path on the binary Tree: V a1 a2 a3 ... an... (Fig.1.)

The rather known cognitive image of the last representation of all real numbers x Î D is shown in Fig. 1.

ITS ROOTS ARE AT THE TOP,
ITS BRANCHES ARE AT THE BOTTOM
- SUCH IS THE ANCIENT FIG TREE.
IT IS TRUTH, INDEED. IT IS BRAHMAN...
ALL THE WORLDS ARE BASED UPON IT...

[Cognition of Brahman. Katha-Upanishada,II,3]


4Kb

Fig. 1. Cognitive visual model of the real numbers set D at the segment [0,1].



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